Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients
Below we demonstrate how the C^∞-regular properties of heat dynamics with non-unit nonlinear diffusion coefficient can be studied. We consider an infinite dimensional model, describing evolution of unbounded lattice spins R^Z^d. As a main step we provide a construction of corresponding variational p...
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| Date: | 2007 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/10116 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients / A.Val. Antoniouk, A.Vict. Antoniouk // Нелинейные граничные задачи. — 2007. — Т. 17. — С. 101-129. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862544603059585024 |
|---|---|
| author | Antoniouk, A.Val. Antoniouk, A.Vict. |
| author_facet | Antoniouk, A.Val. Antoniouk, A.Vict. |
| citation_txt | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients / A.Val. Antoniouk, A.Vict. Antoniouk // Нелинейные граничные задачи. — 2007. — Т. 17. — С. 101-129. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| description | Below we demonstrate how the C^∞-regular properties of heat dynamics with non-unit nonlinear diffusion coefficient can be studied. We consider an infinite dimensional model, describing evolution of unbounded lattice spins R^Z^d. As a main step we provide a construction of corresponding variational processes in ℓp(c) spaces with growing weights ck ~ e^a|k|, k belongs Z^d.
Developing the approach of nonlinear estimates on variations, we find sufficient conditions on the nonlinear coefficients of differential equation that lead to C^∞-regularity of solutions with respect to the initial data and C^∞-regularity of corresponding heat semigroup.
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| first_indexed | 2025-11-25T01:06:38Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-10116 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0236-0497 |
| language | English |
| last_indexed | 2025-11-25T01:06:38Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Antoniouk, A.Val. Antoniouk, A.Vict. 2010-07-23T14:28:58Z 2010-07-23T14:28:58Z 2007 Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients / A.Val. Antoniouk, A.Vict. Antoniouk // Нелинейные граничные задачи. — 2007. — Т. 17. — С. 101-129. — Бібліогр.: 11 назв. — англ. 0236-0497 https://nasplib.isofts.kiev.ua/handle/123456789/10116 Below we demonstrate how the C^∞-regular properties of heat dynamics with non-unit nonlinear diffusion coefficient can be studied. We consider an infinite dimensional model, describing evolution of unbounded lattice spins R^Z^d. As a main step we provide a construction of corresponding variational processes in ℓp(c) spaces with growing weights ck ~ e^a|k|, k belongs Z^d.
 Developing the approach of nonlinear estimates on variations, we find sufficient conditions on the nonlinear coefficients of differential equation that lead to C^∞-regularity of solutions with respect to the initial data and C^∞-regularity of corresponding heat semigroup. en Інститут прикладної математики і механіки НАН України Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients Article published earlier |
| spellingShingle | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients Antoniouk, A.Val. Antoniouk, A.Vict. |
| title | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients |
| title_full | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients |
| title_fullStr | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients |
| title_full_unstemmed | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients |
| title_short | Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients |
| title_sort | regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/10116 |
| work_keys_str_mv | AT antonioukaval regularityofinfinitedimensionalheatdynamicsofunboundedlatticespinswithnonconstantdiffusioncoefficients AT antonioukavict regularityofinfinitedimensionalheatdynamicsofunboundedlatticespinswithnonconstantdiffusioncoefficients |